Course Summary

As the name suggests, Math 115 (Calculus I) is the first course in calculus. "Calculus" as a mathematical subject has two central motivating problems, and this course we'll discuss both.

The first of these problems asks how we can find the equation of the line tangent to the graph of a given function. Happily, there are concrete geometric ideas that motivate the solution to this problem, but to put those ideas into practice requires the invention of a new mathematical tool: the limit. We'll introduce and explore the limit as a tool for answering the so-called "tangent line problem." In addition to exploring limits in a handful of contexts, we'll see how this notion of "derivative" can be used to create a new function from our original function, and we'll explore how these two functions are related to each other. We then spend a number of days developing standard rules for differentiation, after which we apply the derivative to answer a handful of questions (e.g., where does a function take on its maximum and minimum values?).

The last part of the class has us asking the second major question in calculus: how does one find the area underneath the graph of a particular function? We'll come up with a way to answer this question that also requires limits. The punchline to the course is that these two seemingly disparate problems --- finding tangent lines and computing area under a curve --- are actually two sides of the same coin. This is made precise in the so-called Fundamental Theorem of Calculus, and we'll put this theory to good use at the close of the course.

The applet below gives you a sneak peak into how we'll be answering the question of computing tangent lines to curves. In the picture, we want the line tangent to the point A along the green curve (this tangent line is sketched for us in black). We'll compute this line by thinking about what happens to the secant line that connects points A and B as B approaches A. As you drag the point B towards the point A, you should find that the red line looks more and more like the black line.

Course Instructor

The professor for this class is Andy Schultz. His office is on the second floor of the Clapp Library, room 255. He will be available to talk with you thirty minutes before class each day, as well as after class upon your request. The instructor is extremely happy to talk with you outside of class, but it's a good idea to send an email to let him know you want to talk. If meeting before or after class doesn't fit with your schedule, contact the instructor to set up a time that does. You can also try dropping by his office to chat; if his door is open and he has time to talk, he'll be more than happy to help you with whatever calculus (or other) questions you have.

You can contact the instructor at . Though he is always happy to receive emails from you with questions or concerns about the course, he can't guarantee that he'll be able to promptly reply to emails late at night or over the weekend. If you do contact the professor by email, please be sure to follow standard email etiquette. In particular, please make sure you include a greeting and signature and avoid abbreviations. If you're contacting him to ask about a problem, please be sure to specify what the problem asks (as opposed to asking something like ``I can't get problem 2 and need your help").